Charged black holes and phase transitions

The thermodynamic behaviour is discussed of a charged black hole in a box in equilibrium with neutral thermal radiation, in the thermodynamic limit (i.e. of a very massive black hole). The heat capacity at constant volume of this system exhibits several types of discontinuities which resemble phase transitions, and in an appropriate phase plane a critical point can be distinguished. The correspondence with normal thermodynamic phase changes is discussed, and various other thought experiments are briefly mentioned.